The spin group of fermions

TL;DR

This paper identifies a special subgroup of Lorentz transformations that preserve both the momentum and spin characteristics of fermions, revealing a continuous symmetry of moving fermions in relativistic physics.

Contribution

It introduces a one-parameter subgroup of Lorentz transformations that leave fermion momentum and spin projection invariant, expanding understanding of fermion symmetry in relativistic frames.

Findings

Existence of a one-parameter subgroup of Lorentz transformations.

Fermions have infinitely many frames with identical momentum and spin projection.

Transformations involve rotations and boosts aligned with spin projection.

Abstract

It was shown that in the small Wigner group there is a one-parameter subgroup of the Lorentz transformations, which leave unchanged not only the momentum of the fermion with spin h/2, but also its spin characteristics. This is the group of symmetry transformations of the moving fermion. These transformations consist of rotations around the projection axis of the spin and boosts coordinated with them. In other words, there are infinitely many frames of reference in which the fermion has the same momentum and the same spin projection onto the selected axis, although these frames move relative to each other and have been rotated relative to each other.